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# Is a nonzero integer Z prime? (1) |Z|^|Z|=4 (2) |Z^Z|=Z^2

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SVP
Joined: 03 Feb 2003
Posts: 1603

Kudos [?]: 308 [0], given: 0

Is a nonzero integer Z prime? (1) |Z|^|Z|=4 (2) |Z^Z|=Z^2 [#permalink]

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10 Jun 2003, 00:35
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Question Stats:

25% (00:37) correct 75% (00:00) wrong based on 5 sessions

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Is a nonzero integer Z prime?

(1) |Z|^|Z|=4
(2) |Z^Z|=Z^2

Kudos [?]: 308 [0], given: 0

SVP
Joined: 03 Feb 2003
Posts: 1603

Kudos [?]: 308 [0], given: 0

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13 Jun 2003, 07:12
KSS wrote:
D. ?

D is ABSOLUTELY wrong. I think it was a blind guess, no?

Kudos [?]: 308 [0], given: 0

Intern
Joined: 03 Feb 2003
Posts: 7

Kudos [?]: [0], given: 0

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13 Jun 2003, 10:06
I think it is B

a) Z=2 or Z=-2 - not sufficient
b) if Z=2 |Z^Z|=|2^2|=2^2=4; Z^2=4

if Z=-2 |Z^Z|=|(-2)^(-2)|=|(1/-2)^2|=1/4; Z^2=4

so, Z=2 - sufficient

Kudos [?]: [0], given: 0

Manager
Joined: 12 Mar 2003
Posts: 59

Kudos [?]: 1 [0], given: 0

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13 Jun 2003, 10:32
I like this one, excellent !

Ans : C, Yes

1) Z = 2 or -2

2) Z = 1 or 2

Combined : z = 2

Kudos [?]: 1 [0], given: 0

SVP
Joined: 03 Feb 2003
Posts: 1603

Kudos [?]: 308 [0], given: 0

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13 Jun 2003, 12:29
It is C, but many of you wrong anyway.

(1) Z=2 (prime) or -2 (not prime) Thus, not enough.
(2) Z= 1( not prime), -1 (not prime), 2 (prime), Thus, not OK again.

Combine: Z=2, which is OK. The answer, therefore, is C.

I am shoked guys--you lose and add so many extraneous roots!

Kudos [?]: 308 [0], given: 0

Director
Joined: 03 Jul 2003
Posts: 651

Kudos [?]: 106 [0], given: 0

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12 Jul 2003, 19:21
Great problem and great solution!
Is there any rule or trick to make sure one gets all the roots
for an given equation?

Kudos [?]: 106 [0], given: 0

SVP
Joined: 03 Feb 2003
Posts: 1603

Kudos [?]: 308 [0], given: 0

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13 Jul 2003, 12:36
Actually, there is no any special trick for such a question, save for simple checking simple integers, such as 0, 1, -1, 2, -2 and so on.

The most important part of the given question is to remember that 2 is a prime. The smallest one, but a prime even so. 1 and 0 are not primes as are not all negative integers.

Kudos [?]: 308 [0], given: 0

TOEFL Forum Moderator
Joined: 16 Nov 2010
Posts: 1603

Kudos [?]: 601 [0], given: 40

Location: United States (IN)
Concentration: Strategy, Technology

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22 Mar 2011, 20:38
(1)

Z is 2 or -2

So not sufficient

(2)

Z^Z is +ve

|(-1)^-1| = (-1)^2

|1^1| = 1^2 - non-prime

|2^2| = 2^2 - prime

-2 does not fulfil this though

So not sufficient

(1) and (2) together

Z = 2, hence answer is C.
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Kudos [?]: 601 [0], given: 40

Manager
Joined: 05 Jan 2011
Posts: 169

Kudos [?]: 198 [0], given: 8

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22 Mar 2011, 20:50
From 1: Z =2,-2
From 2: z =1,2
So Z=2 (Common terem)
C

Kudos [?]: 198 [0], given: 8

Re: DS: PRIME   [#permalink] 22 Mar 2011, 20:50
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